vlib/math: Add a pure V backend for vlib/math (#11267)

vlib/math/floor.v

@@ -0,0 +1,105 @@
+module math
+
+// floor returns the greatest integer value less than or equal to x.
+//
+// special cases are:
+// floor(±0) = ±0
+// floor(±inf) = ±inf
+// floor(nan) = nan
+pub fn floor(x f64) f64 {
+	if x == 0 || is_nan(x) || is_inf(x, 0) {
+		return x
+	}
+	if x < 0 {
+		mut d, fract := modf(-x)
+		if fract != 0.0 {
+			d = d + 1
+		}
+		return -d
+	}
+	d, _ := modf(x)
+	return d
+}
+
+// ceil returns the least integer value greater than or equal to x.
+//
+// special cases are:
+// ceil(±0) = ±0
+// ceil(±inf) = ±inf
+// ceil(nan) = nan
+pub fn ceil(x f64) f64 {
+	return -floor(-x)
+}
+
+// trunc returns the integer value of x.
+//
+// special cases are:
+// trunc(±0) = ±0
+// trunc(±inf) = ±inf
+// trunc(nan) = nan
+pub fn trunc(x f64) f64 {
+	if x == 0 || is_nan(x) || is_inf(x, 0) {
+		return x
+	}
+	d, _ := modf(x)
+	return d
+}
+
+// round returns the nearest integer, rounding half away from zero.
+//
+// special cases are:
+// round(±0) = ±0
+// round(±inf) = ±inf
+// round(nan) = nan
+pub fn round(x f64) f64 {
+	if x == 0 || is_nan(x) || is_inf(x, 0) {
+		return x
+	}
+	// Largest integer <= x
+	mut y := floor(x) // Fractional part
+	mut r := x - y // Round up to nearest.
+	if r > 0.5 {
+		unsafe {
+			goto rndup
+		}
+	}
+	// Round to even
+	if r == 0.5 {
+		r = y - 2.0 * floor(0.5 * y)
+		if r == 1.0 {
+			rndup:
+			y += 1.0
+		}
+	}
+	// Else round down.
+	return y
+}
+
+// round_to_even returns the nearest integer, rounding ties to even.
+//
+// special cases are:
+// round_to_even(±0) = ±0
+// round_to_even(±inf) = ±inf
+// round_to_even(nan) = nan
+pub fn round_to_even(x f64) f64 {
+	mut bits := f64_bits(x)
+	mut e_ := (bits >> shift) & mask
+	if e_ >= bias {
+		// round abs(x) >= 1.
+		// - Large numbers without fractional components, infinity, and nan are unchanged.
+		// - Add 0.499.. or 0.5 before truncating depending on whether the truncated
+		// number is even or odd (respectively).
+		half_minus_ulp := u64(u64(1) << (shift - 1)) - 1
+		e_ -= u64(bias)
+		bits += (half_minus_ulp + (bits >> (shift - e_)) & 1) >> e_
+		bits &= frac_mask >> e_
+		bits ^= frac_mask >> e_
+	} else if e_ == bias - 1 && bits & frac_mask != 0 {
+		// round 0.5 < abs(x) < 1.
+		bits = bits & sign_mask | uvone // +-1
+	} else {
+		// round abs(x) <= 0.5 including denormals.
+		bits &= sign_mask // +-0
+	}
+	return f64_from_bits(bits)
+}